What is the integral of e^{(3x)/4} ?

The integral of e^{(3x)/4} is 4/3 e^{(3x)/4}+C

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integral of e^{(3x)/4}

\int e^{\frac{3 x}{4}} d x

\frac{4}{3} e^{\frac{3 x}{4}} + C

Solution steps

\int e^{\frac{3 x}{4}} d x

Apply u-substitution

: \int e^{u} \frac{4}{3} d u

= \int e^{u} \frac{4}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{4}{3} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{4}{3} e^{u}

Substitute back

u = \frac{3 x}{4}

= \frac{4}{3} e^{\frac{3 x}{4}}

Add a constant to the solution

= \frac{4}{3} e^{\frac{3 x}{4}} + C

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What is the integral of e^{(3x)/4} ?
The integral of e^{(3x)/4} is 4/3 e^{(3x)/4}+C